2018-09-22T01:49:06Z
http://bims.iranjournals.ir/?_action=export&rf=summon&issue=79
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Bulletin of the Iranian Mathematical Society
2015
12
01
http://bims.iranjournals.ir/article_716_8e575f798bb54dd09730ffab14bfdb1b.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Photo of Heydar Radjavi
2015
12
01
http://bims.iranjournals.ir/article_717_66bd7294a3f29e0f9c99d8a50ccd0009.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
The existence and uniqueness of Heydar Radjavi
2015
12
01
1
14
http://bims.iranjournals.ir/article_718_e909c6cadd11b5194660a75d1c14cf74.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Upper and lower bounds for numerical radii of block shifts
P. Y.
Wu
H.-L.
Gau
For an n-by-n complex matrix A in a block form with the (possibly) nonzero blocks only on the diagonal above the main one, we consider two other matrices whose nonzero entries are along the diagonal above the main one and consist of the norms or minimum moduli of the diagonal blocks of A. In this paper, we obtain two inequalities relating the numeical radii of these matrices and also determine when either of them becomes an equality.
Numerical radius
block shift
minimum modulus
2015
12
01
15
27
http://bims.iranjournals.ir/article_719_7b89cecc3c9d266bd2d8a5e08a8dc1cb.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Higher numerical ranges of matrix polynomials
Gh.
Aghamollaei
M. A.
Nourollahi
Let $P(lambda)$ be an $n$-square complex matrix polynomial, and $1 leq k leq n$ be a positive integer. In this paper, some algebraic and geometrical properties of the $k$-numerical range of $P(lambda)$ are investigated. In particular, the relationship between the $k$-numerical range of $P(lambda)$ and the $k$-numerical range of its companion linearization is stated. Moreover, the $k$-numerical range of the basic $A$-factor block circulant matrix, which is the block companion matrix of the matrix polynomial $P(lambda) = lambda ^m I_n - A$, is studied.
$k$-Numerical range
matrix polynomial
companion linearization
basic $A$-factor block
circulant matrix
2015
12
01
29
45
http://bims.iranjournals.ir/article_720_27058d5330da2190ea9a4d45104b7f64.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
On nest modules of matrices over division rings
B. R.
Yahaghi
M.
Rahimi-Alangi
Let $ m , n in mathbb{N}$, $D$ be a division ring, and $M_{m times n}(D)$ denote the bimodule of all $m times n$ matrices with entries from $D$. First, we characterize one-sided submodules of $M_{m times n}(D)$ in terms of left row reduced echelon or right column reduced echelon matrices with entries from $D$. Next, we introduce the notion of a nest module of matrices with entries from $D$. We then characterize submodules of nest modules of matrices over $D$ in terms of certain finite sequences of left row reduced echelon or right column reduced echelon matrices with entries from $D$. We use this result to characterize principal submodules of nest modules. We also describe subbimodules of nest modules of matrices. As a consequence, we characterize (one-sided) ideals of nest algebras of matrices over division rings.
Bimodule of rectangular matrices over a division ring
(left/right) submodule
subbimodule
(one-sided) ideal
nest modules
2015
12
01
47
63
http://bims.iranjournals.ir/article_721_5f9a18056601fd0fd44a34d75a22addd.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Self-commutators of composition operators with monomial symbols on the Bergman space
A.
Abdollahi
S.
Mehrangiz
T.
Roientan
Let $varphi(z)=z^m, z in mathbb{U}$, for some positive integer $m$, and $C_varphi$ be the composition operator on the Bergman space $mathcal{A}^2$ induced by $varphi$. In this article, we completely determine the point spectrum, spectrum, essential spectrum, and essential norm of the operators $C^*_varphi C_varphi, C_varphi C^*_varphi$ as well as self-commutator and anti-self-commutators of $C_varphi$. We also find the eigenfunctions of these operators.
Bergman space
composition operator
essential spectrum
essential norm
self-commutator
2015
12
01
65
76
http://bims.iranjournals.ir/article_722_d5ce5eefb15ab5a75efe1e6a099e23e5.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Linear maps preserving or strongly preserving majorization on matrices
F.
Khalooei
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear preservers and all linear strong preservers of $prec_{ell s}$ and $sim_{ell s}$ from $M_{nm}$ to $M_{nm}$.
Linear preserver
row substochastic matrix
matrix majorization
2015
12
01
77
83
http://bims.iranjournals.ir/article_723_2527aef09e5df50b63467d24125b54c8.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Additive maps on C$^*$-algebras commuting with $|.|^k$ on normal elements
Y.
Guan
C.
Wang
J.
Hou
Let $mathcal {A} $ and $mathcal {B} $ be C$^*$-algebras. Assume that $mathcal {A}$ is of real rank zero and unital with unit $I$ and $k>0$ is a real number. It is shown that if $Phi:mathcal{A} tomathcal{B}$ is an additive map preserving $|cdot|^k$ for all normal elements; that is, $Phi(|A|^k)=|Phi(A)|^k $ for all normal elements $Ainmathcal A$, $Phi(I)$ is a projection, and there exists a positive number $c$ such that $Phi(iI)Phi(iI)^{*}leq
cPhi(I)Phi(I)^{*}$, then $Phi$ is the sum of a linear Jordan *-homomorphism and a conjugate-linear Jordan *-homomorphism. If, moreover, the map $Phi$ commutes with $|.|^k$ on $mathcal{A}$, then $Phi$ is the sum of a linear *-homomorphism and a conjugate-linear *-homomorphism. In the case when $k not=1$, the assumption $Phi(I)$ being a projection can be deleted.
C$^*$-algebras
additive maps
Jordan homomorphism
*-homomorphism
2015
12
01
85
98
http://bims.iranjournals.ir/article_724_15cc6b48cc93f3f328eb35b3ec30359a.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
A Haar wavelets approach to Stirling's formula
M.
Ahmadinia
H.
Naderi Yeganeh
This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.
Haar wavelets
Parseval's identity
Stirling's formula
2015
12
01
99
106
http://bims.iranjournals.ir/article_725_4334fc7b24c523ffe166068cee677ed5.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Additivity of maps preserving Jordan $eta_{ast}$-products on $C^{*}$-algebras
A.
Taghavi
H.
Rohi
V.
Darvish
Let $mathcal{A}$ and $mathcal{B}$ be two $C^{*}$-algebras such that $mathcal{B}$ is prime. In this paper, we investigate the additivity of maps $Phi$ from $mathcal{A}$ onto $mathcal{B}$ that are bijective, unital and satisfy $Phi(AP+eta PA^{*})=Phi(A)Phi(P)+eta Phi(P)Phi(A)^{*},$ for all $Ainmathcal{A}$ and $Pin{P_{1},I_{mathcal{A}}-P_{1}}$ where $P_{1}$ is a nontrivial projection in $mathcal{A}$. If $eta$ is a non-zero complex number such that $|eta|neq1$, then $Phi$ is additive. Moreover, if $eta$ is rational then $Phi$ is $ast$-additive.
Maps preserving Jordan $eta*$-product
Additive
Prime C*-algebras
2015
12
01
107
116
http://bims.iranjournals.ir/article_726_46c90e129f3d8ce0cb2d465e7884246d.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
A note on lifting projections
D.
Hadwin
Suppose $pi:mathcal{A}rightarrow mathcal{B}$ is a surjective unital $ast$-homomorphism between C*-algebras $mathcal{A}$ and $mathcal{B}$, and $0leq aleq1$ with $ain mathcal{A}$. We give a sufficient condition that ensures there is a proection $pin mathcal{A}$ such that $pi left( pright) =pi left( aright) $. An easy consequence is a result of [L. G. Brown and G. k. Pedersen, C*-algebras of real rank zero, textit{J. Funct. Anal.} {99} (1991) 131--149] that such a $p$ exists when $mathcal{A}$ has real rank zero.
C*-algebra
projection
2015
12
01
117
122
http://bims.iranjournals.ir/article_727_582e0ada23e3758cdf98387770deec3b.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Toeplitz transforms of Fibonacci sequences
L.
Connell
M.
Levine
B.
Mathes
J.
Sukiennik
We introduce a matricial Toeplitz transform and prove that the Toeplitz transform of a second order recurrence sequence is another second order recurrence sequence. We investigate the injectivity of this transform and show how this distinguishes the Fibonacci sequence among other recurrence sequences. We then obtain new Fibonacci identities as an application of our transform.
Hankel transform
Fibonacci numbers
Fibonacci identities
2015
12
01
123
132
http://bims.iranjournals.ir/article_728_fac81767727c4a836e2fc2d91f8e8fed.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
A note on approximation conditions, standard triangularizability and a power set topology
L.
Livshits
The main result of this article is that for collections of entry-wise non-negative matrices the property of possessing a standard triangularization is stable under approximation. The methodology introduced to prove this result allows us to offer quick proofs of the corresponding results of [B. R. Yahaghi, Near triangularizability implies triangularizability, Canad. Math. Bull. 47, (2004), no. 2, 298--313], and [A. A. Jafarian, H. Radjavi, P. Rosenthal and A. R. Sourour, Simultaneous, triangularizability, near commutativity and Rota's theorem, Trans. Amer. Math. Soc. 347, (1995), no. 6, 2191--2199] on the approximations and triangularizability of collections of operators and matrices. In conclusion we introduce and explore a related topology on the power sets of metric spaces.
Simultaneous triangularizability
positive matrices
standard invariant subspaces
semigroups of operators
2015
12
01
133
153
http://bims.iranjournals.ir/article_729_835c889d67bcda2cd2d6f303459aa8e6.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Addendum to: "Infinite-dimensional versions of the primary, cyclic and Jordan decompositions", by M. Radjabalipour
H.
Fan
D.
Hadwin
In his paper mentioned in the title, which appears in the same issue of this journal, Mehdi Radjabalipour derives the cyclic decomposition of an algebraic linear transformation. A more general structure theory for linear transformations appears in Irving Kaplansky's lovely 1954 book on infinite abelian groups. We present a translation of Kaplansky's results for abelian groups into the terminology of linear transformations. We add an additional translation of a ring-theoretic result to give a characterization of algebraically hyporeflexive transformations and the strict closure of the set of polynomials in a transformation $T$.
Abelian group
PID
Module
cyclic
torsion
locally algebraic
hyporeflexive
scalar-reflexive ring
strict topology
2015
12
01
155
173
http://bims.iranjournals.ir/article_730_312c207f682f4959e07b53c8cfb5db04.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Infinite-dimensional versions of the primary, cyclic and Jordan decompositions
M.
Radjabalipour
The famous primary and cyclic decomposition theorems along with the tightly related rational and Jordan canonical forms are extended to linear spaces of infinite dimensions with counterexamples showing the scope of extensions.
Jordan canonical form
rational canonical form
splitting field
2015
12
01
175
183
http://bims.iranjournals.ir/article_731_9998ee94b22e27881824a5bc4920c986.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
Submajorization inequalities associated with $tau$-measurable operators
J.
Zhao
J.
Wu
The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..
Submajorization
von Neumann algebra
$tau$-measurable operators
2015
12
01
185
194
http://bims.iranjournals.ir/article_732_bff972f6998e185187ad5bd0a9ee72b7.pdf
Bulletin of the Iranian Mathematical Society
BIMS
1017-060X
1017-060X
2015
41
Issue 7 (Special Issue)
The witness set of coexistence of quantum effects and its preservers
K.
He
F. G.
Sun
J.
Hou
Q.
Yuan
One of unsolved problems in quantum measurement theory is to characterize coexistence of quantum effects. In this paper, applying positive operator matrix theory, we give a mathematical characterization of the witness set of coexistence of quantum effects and obtain a series of properties of coexistence. We also devote to characterizing bijective morphisms on quantum effects leaving the witness set invariant. Furthermore, applying linear maps preserving commutativity, which are characterized by Choi, Jafarian and Radjavi [Linear maps preserving commutativity, Linear Algebra Appl. 87 (1987), 227--241.], we classify multiplicative general morphisms leaving the witness set invariant on finite dimensional Hilbert space effect algebras.
Positive operator matrices
Coexistence
Hilbert space effect algebras
Isomorphisms
2015
12
01
195
204
http://bims.iranjournals.ir/article_733_11e420ffa346edde192a2c50f80bc9b4.pdf